I disagree with your sentiment about Google News. I think it does a great job of aggregating all the sources to a given headline. It even goes as far as labeling the sources as "Opinion pieces", "Highly Cited", or even "From ___" opposing entity sources (eg. From Saudi Arabia sources).

There is no easy answer to to display ONLY unbiased sources, because that would require an unbiased source to pull from. Which I don't believe exists. With Google News, responsibility falls on the reader to use the sources in front of them to formulate an educated opinion and gain an understanding of the story. If a reader chooses to only view either right-wing or leftist sources via Google News, then that's beyond Google's control.